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Simple simulation of diffusion bridges with application to likelihood inference for diffusions

Author

Listed:
  • Mogens Bladt

    () (Universidad Nacional Autónoma de México)

  • Michael Sørensen

    () (University of Copenhagen and CREATES)

Abstract

With a view to likelihood inference for discretely observed diffusion type models, we propose a simple method of simulating approximations to diffusion bridges. The method is applicable to all one-dimensional diffusion processes and has the advantage that simple simulation methods like the Euler scheme can be applied to bridge simulation. Another advantage over other bridge simulation methods is that the proposed method works well when the diffusion bridge is defined in a long interval because the computational complexity of the method is linear in the length of the interval. In a simulation study we investigate the accuracy and efficiency of the new method and compare it to exact simulation methods. In the study the method provides a very good approximation to the distribution of a diffusion bridge for bridges that are likely to occur in applications to likelihood inference. To illustrate the usefulness of the new method, we present an EM-algorithm for a discretely observed diffusion process. We demonstrate how this estimation method simplifies for exponential families of diffusions and very briefly consider Bayesian inference.

Suggested Citation

  • Mogens Bladt & Michael Sørensen, 2010. "Simple simulation of diffusion bridges with application to likelihood inference for diffusions," CREATES Research Papers 2010-32, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-32
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    File URL: ftp://ftp.econ.au.dk/creates/rp/10/rp10_32.pdf
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    Keywords

    Bayesian inference; diffusion bridge; discretely sampled diffusions; EM-algorithm; Euler scheme; likelihood inference; time-reversion;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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